This article is cited in 2 papers

The discrete spectrum of the Laplace operator on the fundamental domain of the modular group and the Chebyshev psi-function

D. A. Popov

Lomonosov Moscow State University, Belozersky Research Institute of Physico-Chemical Biology

Abstract: An explicit formula is obtained expressing the Chebyshev psi-function in terms of the discrete spectrum of the Laplace operator on the fundamental domain of the modular group.

Keywords: Selberg formula, spectrum of the Laplace operator, Chebyshev psi-function, modular group.

UDC: 511.331+515.178.1

MSC: Primary 11M36; Secondary 11F03

Received: 07.03.2018

DOI: 10.4213/im8783

 English version: Izvestiya: Mathematics, 2019, 83:5, 1066–1079

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